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Finding the Equation of a Line Given the Slope and One Point · Physics Playground

Exercises Equations and inequalities

Example 10 from Algebra and Trigonometry, 2.2 Linear Equations in One Variable

Finding the Equation of a Line Given the Slope and One Point

Write the equation of the line with slope $m = −3$ and passing through the point $(4, 8) .$ Write the final equation in slope-intercept form.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Using the point-slope formula, substitute $−3$ for m and the point $(4, 8)$ for $(x_{1}, y_{1}) .$

$\begin{matrix} y - y_{1} & = & m (x - x_{1}) \\ y - 8 & = & −3 (x - 4) \\ y - 8 & = & −3 x + 12 \\ y & = & −3 x + 20 \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given $m = 4,$ find the equation of the line in slope-intercept form passing through the point $(2, 5) .$

How did it go?

PreviousIdentifying the Slope and y-intercept of a Line Given an Equation Next Finding the Equation of a Line Passing Through Two Given Points

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Solution

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